Revd Greener, who has served the diocese for 14 years and has helped to deliver Wakefield Cathedral's £7.5m regeneration project, will leave his role in November,
During his time he has also supported the Wakefield Rent Deposit Scheme, helping young people out of homelessness and has introduced a new coffee shop, gift shop and a visitor information point at the cathedral.
He said: "One of the issues for Wakefield alongside poverty in the pocket, has been poverty of opportunity and aspiration.
“In my time here, I have seen Wakefield becoming the city of which its citizens can be genuinely proud.
“And I too am proud to have played a part in renewing the cathedral for the people of our city and district and proud to leave a cathedral in such good state."
Supported with cash from the Heritage Lottery Fund, Revd Greener wanted to renew the building and open it to new people.
His wife Pamela also helped when she became a Youtube sensation with her musical talents and song The VAT Ditty. It warned that the then Chancellor's proposals to close VAT relief on historic buildings would put an extra £200,000 on the restoration bill at Wakefield Cathedral - and plunge many other church buildings into financial crisis.
Her campaign helped raise the issue for both Wakefield Cathedral and the Church of England and saw a U-turn from the government.
Most of Rved Greener’s ministry has been in the Wakefield area. He was the Archdeacon of Pontefract for four years and chaired the Board of Education in the historic diocese of Wakefield before being appointed the Dean of Wakefield ten years ago.
He is also an executive member of the Association of English Cathedrals and a Church Commissioner.
The Sub Dean of Wakefield, Canon Tony Macpherson who has worked alongside Revd Greener, said: “Jonathan has given us inspiring leadership over the last 10 years and has led the cathedral in its physical transformation through two large Heritage Lottery Fund projects and a number of smaller ones.
“In his inaugural sermon he spoke of his desire to make the cathedral a meeting place for everyone and we are very grateful for all he has done to help us move towards this.
“We wish Jonathan and Pamela well in their new adventure and will keep them in our prayers.”
Revd Greener's final Sunday in Wakefield is November 5.
He will be installed as the 71st Dean of Exeter, succeeding the Very Revd Jonathan Draped who resigned at the end of August, on November 26.
He said: “It is exciting moving because of challenges of the new post, but it is very hard leaving Wakefield where my life has been for the last 14 years, and where together we’ve managed to achieve some things and deliver a cathedral fit for the 21st century.
“It’s been hard work, as all those who have worked alongside me know only too well. But it’s also been immensely rewarding as has been living in Wakefield at this time while so many good things have come to the city; the new Bull Ring, the renewal of our railway stations, our civic centre, our lovely little theatre, Unity Works, Trinity Walk, Yorkshire Sculpture Park and of course The Hepworth.
“It feels like this city needs fresh eyes and new energy to take the cathedral and its people on the next stage of its journey."
The Anglican Diocesan Bishop of Leeds, Bishop Nick Baines said Revd Greener would bring "gifts of vision, resilience and collegiality" to his new ministry.
“Exeter is receiving a Dean who has helped shape a new way of exercising cathedral ministry in a diocese going through considerable change" he said. "I will miss his creativity, friendship and support.”